Mathematical Research Letters
Volume 15 (2008)
Spectrum of the Laplacian on manifolds with Spin(9) holonomy
Pages: 1167 – 1186
We consider noncompact complete manifolds with Spin(9) holonomy and proved an one end result and a splitting type theorem under different conditions on the bottom of the spectrum. We proved that any harmonic functions with finite Dirichlet integral must be Cayley-harmonic, which allowed us to conclude an one end result. In the second part, we established a splitting type theorem by utilizing the Busemann function.